In this work, we have investigated the behavior under shear and compression of mica surfaces coated with poly(N-isopropylacrylamide) cationic microgels. We have observed the emergence of velocity dependent, shear-induced normal forces, which can be large enough to entrain a fluid film that separates the surfaces out of contact, driving the dynamic system from conditions of boundary to hydrodynamic lubrication. By implementing a feedback-loop control on the surface separation, we were able to quantify the magnitude of the lift force as a function of the surface separation and driving speed. Our results illustrate how elastohydrodynamic effects can play an important role in the lubrication of compliant surfaces, providing pathways for control of friction and wear.